Answer to Question #328714 in Statistics and Probability for Tenshi

Question

The average time it takes a group of college students to complete a certain examination is 32 minutes. The standard deviation is 6 minutes. Assume that the variable is normally distributed.

If 64 randomly selected college students take the examination, what is the probability that the mean time it takes the group to complete the test will be less than 36 minutes?

Answer 1

X~$N(32,({\frac 6 {\sqrt{64}}})^2)$

$P(X<36)=P(N(32,({\frac 6 {\sqrt{64}}})^2)<36)=P(32+0.75Z<36)=P(Z<5.33)\approx1$